Large-scale Uncertainty Quantification for Latent Variable Models Using Subsampling Markov Chain Monte Carlo

• URL: http://arxiv.org/abs/2606.00309v1
• Date: Fri, 29 May 2026 19:34:28 GMT
• Title: Large-scale Uncertainty Quantification for Latent Variable Models Using Subsampling Markov Chain Monte Carlo
• Abstract summary: We develop a statistical scaling limit theory for SGLD--Gibbs.<n>We show that global parameters converge to a diffusion-type limit, while each latent variable converges to a jump process, reflecting the use of intermittent Gibbs updates.
• Score: 5.432885556835047
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Stochastic gradient Langevin dynamics combined with Gibbs updates (SGLD--Gibbs) provides a highly scalable approach to approximate Bayesian inference in latent variable models. However, it remains unclear how to tune the algorithm's hyperparameters in a principled manner to ensure the uncertainty estimates are statistically meaningful. In this work, we address this gap in tuning guidance by developing a statistical scaling limit theory for SGLD--Gibbs. We derive a joint asymptotic limit for the global parameters and latent variables under appropriate space-time rescaling. We show that global parameters converge to a diffusion-type limit, while each latent variable converges to a jump process, reflecting the use of intermittent Gibbs updates. This joint jump-diffusion structure reveals how latent-variable randomness contributes to the stationary distribution of the global parameters. We leverage our results to propose explicit guidance on hyperparameter tuning for SGLD--Gibbs that ensures meaningful uncertainty quantification. Numerical experiments show that SGLD--Gibbs with our tuning guidance leads to better parameter estimates, uncertainty quantification, and predictive performance than stochastic variational inference.

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